Electrochemistry for Engineers LECTURE 11 Lecturer: Dr. Brian Rosen Office: 128 Wolfson Office Hours: Sun 16:00

Photoelectrochemical Cells (PECs)

Energy Balance

Figures of Merit for PEC’s

Photoelectrochemical Cell (PEC)

Molecular Orbital Theory

MO Theory Applied to Semiconductors e- h+h+ “Electron-hole pair”

Bandgaps for Common Semiconductors * eV = 0 is vs. the energy of a single electron in a vacuum

Covalent vs. Ionic Semiconductors Covalent (E g represents energy gap between bonding and antibonding orbitals of same symmetry) – Silicon VB made up of bonding π orbitals CB made up of antibonding π* orbitals Ionic (E g represents energy gap between completely different orbitals) – Titanium dioxide (TiO 2 ) VB made up of filled 2p orbitals of O 2- CV made up of empty 2d orbitals of Ti +4 – More stable towards corrosion since ionic band gaps are generally larger and material is less reactive

Sunlight under AM 1.5

Bandgap Size Optimization If hv > E g, the extra energy will readily thermalize and the electron will drop down to the conduction band edge, E cb If hv = E g, the electron will excite to t he conduction band edge, E cb Optimal range for solar energy adsorption is therefore between 1.1 and 1.7eV

Beer’s Law Applied to Semiconductors Si I0I0 I z Io = Incident light intensity I = Transmitted light intensity z = optical path length (not thickness!) A = Absorbance T = Transmittance Α = absorption coefficient (function of wavelength!!)

Direct vs. Indirect Gap Direct Gap – fully allowed (optical, spin) transition (GaAs, CdTe) Indirect Gap- optically forbidden transitions near the band are only made possible by coupling with photon momentum and molecular vibrations (Si, TiO 2 )

Carriers in Intrinsic Semiconductors Thermal energy will always excite valence electrons into the conduction band (except at 0K) Hole moving towards a contact is equivalent to an electron moving away e- h+h+ Eg = bandgap in eV k = boltzman constant T = absolute temperature n i = electron concentration in intrinsic material [cm -3 ] p i = hole concentration in intrinsic material [cm -3 ]

e- h+h+ An electron in the conduction band MUST create a hole in the valence band, therefore the carrier concentration is Carriers in Intrinsic Semiconductors n 2 at room temperature for Si (relatively low band gap) comes to a carrier concentration less than 1 part per billion; Therefore, we must utilize doping to increase the conductance

Semiconductor Doping Ability to change the Fermi Level of the electrode Increasing the conductivity such that photo- generated electrons and holes can travel larger distances without resistive losses

Semiconductor Doping n-type doping replaces native atoms with an atom containing an extra electron than itself – Electrons are majority carrier, holes are minority carrier p-type doping replaces native atoms with an atom containing one less electron than itself – Holes are majority carrier, electrons are minority carrier n-type p-type

Shallow Donors and Acceptors Shallow n-type Donor energy level is near the conduction band edge of the native material p-type Acceptor energy level is near the valence band edge of the native material Shallow donors and acceptors are generally fully ionized at room temperature! Si 1.12 eV

Semiconductor-Liquid Junction and Depletion Depth, W Electric field generation at the interface allows for charge separation! The number of states in solution far exceeds that in the semiconductor, therefore, the energy of the solution will not change appreciably W

Electric Field inside the Depletion Layer In the bulk, a negative test change does not feel the interface because the positive charges in the depletion layer screen the negative charge in the liquid As the test charge moves through the depletion layer, the effect of screening is lessened and the electric potential becomes more negative

Band Bending

Built in Voltage, V bi Maximum electric field within the semiconductor after equilibration with the electrolyte Dependent on both semiconductor and electrolyte!

Barrier Height Energy, qφ b XXXXX Φ b = barrier height in volts q Φ b = barrier height in eV

For Experiment Preparation Vbi = built in voltage Nd = number of dopant atoms q = charge of carrier ε = static dielectric constant of semiconductor V(x) = electric potential as a function of depth W

Surface Concentration of Carriers In and n-type semiconductor, electrons (the majority carrier) are depleted within ‘W’, because of less shielding from positive nuclei. electron concentration, n(x): n b = bulk concentration of electrons (per cm 3 ) q = charge of an electron V(x) = electric potential k = Boltzman constant T = Absolute temperature (kelvin)

Accumulation (and Bending)

Accumulation Depletion region in n-type semiconductor is limited by the density of dopant atoms since these atoms are the source of the electrons In accumulation, the extra electron can be in the vicinity of both a dopant atom or a native atom. Accumulation limit is by overall atom density

Semiconductor-Electrolyte Interface (n-type, at Equilibrium)

Semiconductor-Electrolyte Interface (n-type, Oxidizing bias)

Semiconductor-Electrolyte Interface (n-type, Reducing bias)

Semiconductor-Electrolyte Interface (n-type, Illumination) Electrons and holes separate in the electric field, creating an additional field which counteracts and “unbends” the bands - +

- + Electrons and holes separate in the electric field, creating an additional field which counteracts and “unbends” the bands Semiconductor-Electrolyte Interface (p-type, Illumination)

Photoelectrochemical Cell (PEC)

Photoelectrochemistry

Hydrogen Photocathode (Photoelectrochemical Cell) Minority carrier (here, electrons) are driven TOWARDS the interface p-type semiconductor

Oxygen Photocathode (Photoelectrochemical Cell) Minority carrier (here, holes) are driven TOWARDS the interface n-type semiconductor

Oxygen Photocathode (PhotoASSISTED Cell) Minority carrier (here, holes) are driven TOWARDS the interface n-type semiconductor

Photochemical Cell

Dye Sensitized Solar Cell 1.Photon excites electron to conduction band of dye 2.Electron exits the dye (deactivating it) and travels through TiO2 network to anode 3.Electron powers external load 4.Electron reduces triiodine to iodide at cathode 5.Iodide oxidizes at dye (connected to TiO 2 connected to anode) reactivating the dye

Photo-assisted CO 2 Reduction  Photocarriers generated by exposure to light produces up to 450 mV of photovolage Photocurrent is 20x greater  than dark current at low over- potentials Data by BAR, CR, and ASK

Shottky Barrier (Metal – Semiconductor Interface) - +